TSTP Solution File: LCL496+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL496+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:52:43 EDT 2022
% Result : Theorem 19.33s 19.57s
% Output : CNFRefutation 19.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 28
% Syntax : Number of formulae : 110 ( 54 unt; 0 def)
% Number of atoms : 202 ( 70 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 175 ( 83 ~; 73 |; 9 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 239 ( 0 sgn 36 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ) ).
fof(cn1,axiom,
( cn1
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) ) ).
fof(r4,axiom,
( r4
<=> ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ) ).
fof(r5,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ) ).
fof(principia_op_implies_or,axiom,
op_implies_or ).
fof(principia_modus_ponens,axiom,
modus_ponens ).
fof(principia_r4,axiom,
r4 ).
fof(principia_r5,axiom,
r5 ).
fof(luka_cn1,conjecture,
cn1 ).
fof(subgoal_0,plain,
cn1,
inference(strip,[],[luka_cn1]) ).
fof(negate_0_0,plain,
~ cn1,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ cn1
<=> ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) ),
inference(canonicalize,[],[cn1]) ).
fof(normalize_0_1,plain,
! [P,Q,R] :
( ( ~ cn1
| is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) )
& ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_Q_2),implies(implies(skolemFOFtoCNF_Q_2,skolemFOFtoCNF_R_1),implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_R_1))))
| cn1 ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_Q_2),implies(implies(skolemFOFtoCNF_Q_2,skolemFOFtoCNF_R_1),implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_R_1))))
| cn1 ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ cn1,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
( ~ r5
<=> ? [P,Q,R] : ~ is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(canonicalize,[],[r5]) ).
fof(normalize_0_5,plain,
! [P,Q,R] :
( ( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_Q_7,skolemFOFtoCNF_R_3),implies(or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_Q_7),or(skolemFOFtoCNF_P_10,skolemFOFtoCNF_R_3))))
| r5 )
& ( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [P,Q,R] :
( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
r5,
inference(canonicalize,[],[principia_r5]) ).
fof(normalize_0_8,plain,
( ~ op_implies_or
| ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[op_implies_or]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
op_implies_or,
inference(canonicalize,[],[principia_op_implies_or]) ).
fof(normalize_0_11,plain,
( ~ r4
<=> ? [P,Q,R] : ~ is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
inference(canonicalize,[],[r4]) ).
fof(normalize_0_12,plain,
! [P,Q,R] :
( ( ~ is_a_theorem(implies(or(skolemFOFtoCNF_P_9,or(skolemFOFtoCNF_Q_6,skolemFOFtoCNF_R_2)),or(skolemFOFtoCNF_Q_6,or(skolemFOFtoCNF_P_9,skolemFOFtoCNF_R_2))))
| r4 )
& ( ~ r4
| is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [P,Q,R] :
( ~ r4
| is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
r4,
inference(canonicalize,[],[principia_r4]) ).
fof(normalize_0_15,plain,
( ~ modus_ponens
<=> ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(X)
& is_a_theorem(implies(X,Y)) ) ),
inference(canonicalize,[],[modus_ponens]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ( ~ is_a_theorem(skolemFOFtoCNF_Y)
| modus_ponens )
& ( is_a_theorem(implies(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| modus_ponens )
& ( is_a_theorem(skolemFOFtoCNF_X)
| modus_ponens )
& ( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
modus_ponens,
inference(canonicalize,[],[principia_modus_ponens]) ).
cnf(refute_0_0,plain,
( ~ is_a_theorem(implies(implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_Q_2),implies(implies(skolemFOFtoCNF_Q_2,skolemFOFtoCNF_R_1),implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_R_1))))
| cn1 ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ cn1,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
~ is_a_theorem(implies(implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_Q_2),implies(implies(skolemFOFtoCNF_Q_2,skolemFOFtoCNF_R_1),implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_R_1)))),
inference(resolve,[$cnf( cn1 )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ r5
| is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
r5,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))),
inference(resolve,[$cnf( r5 )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
is_a_theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),or(not(X),X_44)))),
inference(subst,[],[refute_0_5:[bind(P,$fot(not(X))),bind(Q,$fot(X_43)),bind(R,$fot(X_44))]]) ).
cnf(refute_0_7,plain,
( ~ op_implies_or
| implies(X,Y) = or(not(X),Y) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
op_implies_or,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
implies(X,Y) = or(not(X),Y),
inference(resolve,[$cnf( op_implies_or )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
implies(X,X_44) = or(not(X),X_44),
inference(subst,[],[refute_0_9:[bind(Y,$fot(X_44))]]) ).
cnf(refute_0_11,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_12,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_13,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( implies(X,X_44) != or(not(X),X_44)
| or(not(X),X_44) = implies(X,X_44) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,X_44))),bind(Y0,$fot(or(not(X),X_44)))]]) ).
cnf(refute_0_15,plain,
or(not(X),X_44) = implies(X,X_44),
inference(resolve,[$cnf( $equal(implies(X,X_44),or(not(X),X_44)) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
( or(not(X),X_44) != implies(X,X_44)
| ~ is_a_theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),or(not(X),X_44))))
| is_a_theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),or(not(X),X_44)))) ),[0,1,1],$fot(implies(X,X_44))]]) ).
cnf(refute_0_17,plain,
( ~ is_a_theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),or(not(X),X_44))))
| is_a_theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_44),implies(X,X_44)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
is_a_theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),or(not(X),X_44)))) )],[refute_0_6,refute_0_17]) ).
cnf(refute_0_19,plain,
( implies(X,Y) != or(not(X),Y)
| or(not(X),Y) = implies(X,Y) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,Y))),bind(Y0,$fot(or(not(X),Y)))]]) ).
cnf(refute_0_20,plain,
or(not(X),Y) = implies(X,Y),
inference(resolve,[$cnf( $equal(implies(X,Y),or(not(X),Y)) )],[refute_0_9,refute_0_19]) ).
cnf(refute_0_21,plain,
or(not(X),X_43) = implies(X,X_43),
inference(subst,[],[refute_0_20:[bind(Y,$fot(X_43))]]) ).
cnf(refute_0_22,plain,
implies(or(not(X),X_43),implies(X,X_44)) = implies(or(not(X),X_43),implies(X,X_44)),
introduced(tautology,[refl,[$fot(implies(or(not(X),X_43),implies(X,X_44)))]]) ).
cnf(refute_0_23,plain,
( implies(or(not(X),X_43),implies(X,X_44)) != implies(or(not(X),X_43),implies(X,X_44))
| or(not(X),X_43) != implies(X,X_43)
| implies(or(not(X),X_43),implies(X,X_44)) = implies(implies(X,X_43),implies(X,X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),X_43),implies(X,X_44)),implies(or(not(X),X_43),implies(X,X_44))) ),[1,0],$fot(implies(X,X_43))]]) ).
cnf(refute_0_24,plain,
( or(not(X),X_43) != implies(X,X_43)
| implies(or(not(X),X_43),implies(X,X_44)) = implies(implies(X,X_43),implies(X,X_44)) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_43),implies(X,X_44)),implies(or(not(X),X_43),implies(X,X_44))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
implies(or(not(X),X_43),implies(X,X_44)) = implies(implies(X,X_43),implies(X,X_44)),
inference(resolve,[$cnf( $equal(or(not(X),X_43),implies(X,X_43)) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))) = implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))),
introduced(tautology,[refl,[$fot(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))))]]) ).
cnf(refute_0_27,plain,
( implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))) != implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44)))
| implies(or(not(X),X_43),implies(X,X_44)) != implies(implies(X,X_43),implies(X,X_44))
| implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))) = implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))),implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44)))) ),[1,1],$fot(implies(implies(X,X_43),implies(X,X_44)))]]) ).
cnf(refute_0_28,plain,
( implies(or(not(X),X_43),implies(X,X_44)) != implies(implies(X,X_43),implies(X,X_44))
| implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))) = implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))),implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44)))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))) = implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44))),
inference(resolve,[$cnf( $equal(implies(or(not(X),X_43),implies(X,X_44)),implies(implies(X,X_43),implies(X,X_44))) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))) != implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44)))
| ~ is_a_theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))))
| is_a_theorem(implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44)))) ),[0],$fot(implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44))))]]) ).
cnf(refute_0_31,plain,
( ~ is_a_theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))))
| is_a_theorem(implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44))),implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44)))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
is_a_theorem(implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_43,X_44),implies(or(not(X),X_43),implies(X,X_44)))) )],[refute_0_18,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ r4
| is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_34,plain,
r4,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_35,plain,
is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))),
inference(resolve,[$cnf( r4 )],[refute_0_34,refute_0_33]) ).
cnf(refute_0_36,plain,
is_a_theorem(implies(or(not(X),or(X_20,X_21)),or(X_20,or(not(X),X_21)))),
inference(subst,[],[refute_0_35:[bind(P,$fot(not(X))),bind(Q,$fot(X_20)),bind(R,$fot(X_21))]]) ).
cnf(refute_0_37,plain,
implies(X,X_21) = or(not(X),X_21),
inference(subst,[],[refute_0_9:[bind(Y,$fot(X_21))]]) ).
cnf(refute_0_38,plain,
( implies(X,X_21) != or(not(X),X_21)
| or(not(X),X_21) = implies(X,X_21) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,X_21))),bind(Y0,$fot(or(not(X),X_21)))]]) ).
cnf(refute_0_39,plain,
or(not(X),X_21) = implies(X,X_21),
inference(resolve,[$cnf( $equal(implies(X,X_21),or(not(X),X_21)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( or(not(X),X_21) != implies(X,X_21)
| ~ is_a_theorem(implies(or(not(X),or(X_20,X_21)),or(X_20,or(not(X),X_21))))
| is_a_theorem(implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),or(X_20,X_21)),or(X_20,or(not(X),X_21)))) ),[0,1,1],$fot(implies(X,X_21))]]) ).
cnf(refute_0_41,plain,
( ~ is_a_theorem(implies(or(not(X),or(X_20,X_21)),or(X_20,or(not(X),X_21))))
| is_a_theorem(implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_21),implies(X,X_21)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
is_a_theorem(implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),or(X_20,X_21)),or(X_20,or(not(X),X_21)))) )],[refute_0_36,refute_0_41]) ).
cnf(refute_0_43,plain,
or(not(X),or(X_20,X_21)) = implies(X,or(X_20,X_21)),
inference(subst,[],[refute_0_20:[bind(Y,$fot(or(X_20,X_21)))]]) ).
cnf(refute_0_44,plain,
implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21))) = implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21))),
introduced(tautology,[refl,[$fot(implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21))))]]) ).
cnf(refute_0_45,plain,
( implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21))) != implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21)))
| or(not(X),or(X_20,X_21)) != implies(X,or(X_20,X_21))
| implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21))) = implies(implies(X,or(X_20,X_21)),or(X_20,implies(X,X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21))),implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21)))) ),[1,0],$fot(implies(X,or(X_20,X_21)))]]) ).
cnf(refute_0_46,plain,
( or(not(X),or(X_20,X_21)) != implies(X,or(X_20,X_21))
| implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21))) = implies(implies(X,or(X_20,X_21)),or(X_20,implies(X,X_21))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21))),implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21)))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21))) = implies(implies(X,or(X_20,X_21)),or(X_20,implies(X,X_21))),
inference(resolve,[$cnf( $equal(or(not(X),or(X_20,X_21)),implies(X,or(X_20,X_21))) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
( implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21))) != implies(implies(X,or(X_20,X_21)),or(X_20,implies(X,X_21)))
| ~ is_a_theorem(implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21))))
| is_a_theorem(implies(implies(X,or(X_20,X_21)),or(X_20,implies(X,X_21)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21)))) ),[0],$fot(implies(implies(X,or(X_20,X_21)),or(X_20,implies(X,X_21))))]]) ).
cnf(refute_0_49,plain,
( ~ is_a_theorem(implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21))))
| is_a_theorem(implies(implies(X,or(X_20,X_21)),or(X_20,implies(X,X_21)))) ),
inference(resolve,[$cnf( $equal(implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21))),implies(implies(X,or(X_20,X_21)),or(X_20,implies(X,X_21)))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
is_a_theorem(implies(implies(X,or(X_20,X_21)),or(X_20,implies(X,X_21)))),
inference(resolve,[$cnf( is_a_theorem(implies(or(not(X),or(X_20,X_21)),or(X_20,implies(X,X_21)))) )],[refute_0_42,refute_0_49]) ).
cnf(refute_0_51,plain,
is_a_theorem(implies(implies(X_31,or(not(X),X_33)),or(not(X),implies(X_31,X_33)))),
inference(subst,[],[refute_0_50:[bind(X,$fot(X_31)),bind(X_20,$fot(not(X))),bind(X_21,$fot(X_33))]]) ).
cnf(refute_0_52,plain,
implies(X,implies(X_31,X_33)) = or(not(X),implies(X_31,X_33)),
inference(subst,[],[refute_0_9:[bind(Y,$fot(implies(X_31,X_33)))]]) ).
cnf(refute_0_53,plain,
( implies(X,implies(X_31,X_33)) != or(not(X),implies(X_31,X_33))
| or(not(X),implies(X_31,X_33)) = implies(X,implies(X_31,X_33)) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(implies(X,implies(X_31,X_33)))),bind(Y0,$fot(or(not(X),implies(X_31,X_33))))]]) ).
cnf(refute_0_54,plain,
or(not(X),implies(X_31,X_33)) = implies(X,implies(X_31,X_33)),
inference(resolve,[$cnf( $equal(implies(X,implies(X_31,X_33)),or(not(X),implies(X_31,X_33))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( or(not(X),implies(X_31,X_33)) != implies(X,implies(X_31,X_33))
| ~ is_a_theorem(implies(implies(X_31,or(not(X),X_33)),or(not(X),implies(X_31,X_33))))
| is_a_theorem(implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_31,or(not(X),X_33)),or(not(X),implies(X_31,X_33)))) ),[0,1],$fot(implies(X,implies(X_31,X_33)))]]) ).
cnf(refute_0_56,plain,
( ~ is_a_theorem(implies(implies(X_31,or(not(X),X_33)),or(not(X),implies(X_31,X_33))))
| is_a_theorem(implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33)))) ),
inference(resolve,[$cnf( $equal(or(not(X),implies(X_31,X_33)),implies(X,implies(X_31,X_33))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
is_a_theorem(implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_31,or(not(X),X_33)),or(not(X),implies(X_31,X_33)))) )],[refute_0_51,refute_0_56]) ).
cnf(refute_0_58,plain,
or(not(X),X_33) = implies(X,X_33),
inference(subst,[],[refute_0_20:[bind(Y,$fot(X_33))]]) ).
cnf(refute_0_59,plain,
implies(X_31,or(not(X),X_33)) = implies(X_31,or(not(X),X_33)),
introduced(tautology,[refl,[$fot(implies(X_31,or(not(X),X_33)))]]) ).
cnf(refute_0_60,plain,
( implies(X_31,or(not(X),X_33)) != implies(X_31,or(not(X),X_33))
| or(not(X),X_33) != implies(X,X_33)
| implies(X_31,or(not(X),X_33)) = implies(X_31,implies(X,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_31,or(not(X),X_33)),implies(X_31,or(not(X),X_33))) ),[1,1],$fot(implies(X,X_33))]]) ).
cnf(refute_0_61,plain,
( or(not(X),X_33) != implies(X,X_33)
| implies(X_31,or(not(X),X_33)) = implies(X_31,implies(X,X_33)) ),
inference(resolve,[$cnf( $equal(implies(X_31,or(not(X),X_33)),implies(X_31,or(not(X),X_33))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
implies(X_31,or(not(X),X_33)) = implies(X_31,implies(X,X_33)),
inference(resolve,[$cnf( $equal(or(not(X),X_33),implies(X,X_33)) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33))) = implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33))),
introduced(tautology,[refl,[$fot(implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33))))]]) ).
cnf(refute_0_64,plain,
( implies(X_31,or(not(X),X_33)) != implies(X_31,implies(X,X_33))
| implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33))) != implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33)))
| implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33))) = implies(implies(X_31,implies(X,X_33)),implies(X,implies(X_31,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33))),implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33)))) ),[1,0],$fot(implies(X_31,implies(X,X_33)))]]) ).
cnf(refute_0_65,plain,
( implies(X_31,or(not(X),X_33)) != implies(X_31,implies(X,X_33))
| implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33))) = implies(implies(X_31,implies(X,X_33)),implies(X,implies(X_31,X_33))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33))),implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33))) = implies(implies(X_31,implies(X,X_33)),implies(X,implies(X_31,X_33))),
inference(resolve,[$cnf( $equal(implies(X_31,or(not(X),X_33)),implies(X_31,implies(X,X_33))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
( implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33))) != implies(implies(X_31,implies(X,X_33)),implies(X,implies(X_31,X_33)))
| ~ is_a_theorem(implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33))))
| is_a_theorem(implies(implies(X_31,implies(X,X_33)),implies(X,implies(X_31,X_33)))) ),
introduced(tautology,[equality,[$cnf( is_a_theorem(implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33)))) ),[0],$fot(implies(implies(X_31,implies(X,X_33)),implies(X,implies(X_31,X_33))))]]) ).
cnf(refute_0_68,plain,
( ~ is_a_theorem(implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33))))
| is_a_theorem(implies(implies(X_31,implies(X,X_33)),implies(X,implies(X_31,X_33)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33))),implies(implies(X_31,implies(X,X_33)),implies(X,implies(X_31,X_33)))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
is_a_theorem(implies(implies(X_31,implies(X,X_33)),implies(X,implies(X_31,X_33)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_31,or(not(X),X_33)),implies(X,implies(X_31,X_33)))) )],[refute_0_57,refute_0_68]) ).
cnf(refute_0_70,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| ~ modus_ponens
| is_a_theorem(Y) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_71,plain,
modus_ponens,
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_72,plain,
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ),
inference(resolve,[$cnf( modus_ponens )],[refute_0_71,refute_0_70]) ).
cnf(refute_0_73,plain,
( ~ is_a_theorem(implies(X_31,implies(X,X_33)))
| ~ is_a_theorem(implies(implies(X_31,implies(X,X_33)),implies(X,implies(X_31,X_33))))
| is_a_theorem(implies(X,implies(X_31,X_33))) ),
inference(subst,[],[refute_0_72:[bind(X,$fot(implies(X_31,implies(X,X_33)))),bind(Y,$fot(implies(X,implies(X_31,X_33))))]]) ).
cnf(refute_0_74,plain,
( ~ is_a_theorem(implies(X_31,implies(X,X_33)))
| is_a_theorem(implies(X,implies(X_31,X_33))) ),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_31,implies(X,X_33)),implies(X,implies(X_31,X_33)))) )],[refute_0_69,refute_0_73]) ).
cnf(refute_0_75,plain,
( ~ is_a_theorem(implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44))))
| is_a_theorem(implies(implies(X,X_43),implies(implies(X_43,X_44),implies(X,X_44)))) ),
inference(subst,[],[refute_0_74:[bind(X,$fot(implies(X,X_43))),bind(X_31,$fot(implies(X_43,X_44))),bind(X_33,$fot(implies(X,X_44)))]]) ).
cnf(refute_0_76,plain,
is_a_theorem(implies(implies(X,X_43),implies(implies(X_43,X_44),implies(X,X_44)))),
inference(resolve,[$cnf( is_a_theorem(implies(implies(X_43,X_44),implies(implies(X,X_43),implies(X,X_44)))) )],[refute_0_32,refute_0_75]) ).
cnf(refute_0_77,plain,
is_a_theorem(implies(implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_Q_2),implies(implies(skolemFOFtoCNF_Q_2,skolemFOFtoCNF_R_1),implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_R_1)))),
inference(subst,[],[refute_0_76:[bind(X,$fot(skolemFOFtoCNF_P_3)),bind(X_43,$fot(skolemFOFtoCNF_Q_2)),bind(X_44,$fot(skolemFOFtoCNF_R_1))]]) ).
cnf(refute_0_78,plain,
$false,
inference(resolve,[$cnf( is_a_theorem(implies(implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_Q_2),implies(implies(skolemFOFtoCNF_Q_2,skolemFOFtoCNF_R_1),implies(skolemFOFtoCNF_P_3,skolemFOFtoCNF_R_1)))) )],[refute_0_77,refute_0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL496+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 2 15:43:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 19.33/19.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.33/19.57
% 19.33/19.57 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.33/19.58
%------------------------------------------------------------------------------